Question

At a very basic level, food and shelter constitute the two most important goods needed to...

At a very basic level, food and shelter constitute the two most important goods needed to sustain human life. Accordingly, assume that a poor person must allocate his income solely between food and shelter.

A. Show that if shelter is an inferior good, food must be a normal good.

B. If food is a normal good, is shelter necessarily an inferior good? Explain, and show your answer graphically.

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Answer #1

a. Let the quantities of food and shelter be denoted by F and S. Then the budget constraint implies Pf*F + Ps*S = M. Differentiating this equation, holding Ps and Pf constant, reveals Pf*dF/dM + Ps*dS/dM = 1.

If shelter is an inferior good, dS/dM < 0, then dF/dM must be positive; food is a normal good if shelter is inferior.

b. If food is a normal good, It need not be the case that shelter necessarily an inferior good. The movement from S to Q means that demand for both shelter and food increased due to the increase in income.

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